Enter any dataset and instantly find its median, mode (including multimodal sets), sorted values, minimum, maximum and range.
Enter a dataset to find its median and mode
A median and mode calculator finds the true "middle" and "most common" values in a dataset in a single step. Enter any list of numbers and this free calculator sorts your data and instantly returns the median, the mode (including bimodal and multimodal sets), the minimum, maximum, and range. Unlike the mean, median and mode are resistant to distortion from extreme values, which makes them the preferred measures of central tendency for skewed real-world data like incomes, home prices, or response times. Whether you need a quick range calculator for a homework problem or a multimodal calculator for survey data with repeated values, this tool shows the full sorted list behind every result.
The median is the middle value of a dataset once it's sorted in ascending order — the value at position (n+1)÷2 for an odd count, or the average of the two middle values for an even count. The mode is simply the value (or values) that occur most frequently. Range, shown alongside them, is the difference between the largest and smallest value, a quick rough measure of spread.
This tool is built for students learning descriptive statistics, teachers comparing measures of central tendency, real estate analysts reporting median home prices, retailers identifying the mode of best-selling sizes or colors, survey researchers summarizing categorical responses, and anyone who needs a fast way to find the median, mode, and range without opening a spreadsheet.
The mean can be pulled far from a "typical" value by just one or two extreme numbers — a single billionaire in a room distorts average income enormously, but not the median income. The mode, meanwhile, is the only measure of central tendency that works on purely categorical data (like favorite color), and it's essential for identifying the single most common outcome in any dataset, numerical or not.
Economists and journalists report median household income and median home price because they resist distortion from a handful of extremely wealthy households or luxury properties. Retailers use mode to stock the most commonly purchased shoe size or shirt color. Teachers compare median test scores against the mean to spot skew caused by a few very low or very high scores. Manufacturers use range as a fast, rough check on measurement consistency before running a full standard deviation analysis.
How this calculator derives each result from your sorted data
Because median only depends on rank position, not magnitude, one extreme value can shift it by at most one sorted position — unlike the mean.
A dataset can have no mode (all values unique), a single mode, or several tied modes — bimodal or multimodal.
Range only uses the two most extreme values, so it's fast but ignores everything in between — standard deviation gives a fuller picture.
From entering data to reading the sorted list
Type or paste your numbers into the Data Set box, separated by commas, spaces, or line breaks.
The calculator sorts your data and computes the median, mode, minimum, maximum, and range instantly.
The highlighted result box shows the median — the middle value, or the average of the two middle values, of your sorted dataset.
Review the most frequent value(s), the smallest and largest values, and the range (max minus min).
Scan the fully sorted list to see exactly how the median and mode were derived from your raw input.
Use the Average Calculator alongside this tool to see whether mean, median, and mode agree or diverge, which can reveal skew in your data.
The calculator's own default dataset: 2, 4, 4, 4, 5, 5, 7, 9
A small dataset of 8 values: 2, 4, 4, 4, 5, 5, 7, 9. We'll find the median, mode, and range, then compare against the odd-length version with the last value dropped.
Explanation: the median (4.5) falls between two data points because n is even, while the mode (4) must be an actual value that appears in the dataset — median and mode do not have to match, and here they are close but not identical.
What it means when mean, median, and mode agree — or diverge
| Pattern | What It Means | Example |
|---|---|---|
| Mean ≈ Median ≈ Mode | Roughly symmetric distribution, no strong skew | Test scores clustered around 75 |
| Mean > Median > Mode | Right-skewed (long tail toward high values) | Household income data |
| Mean < Median < Mode | Left-skewed (long tail toward low values) | Age at retirement in some professions |
| No mode | Every value in the dataset is unique | 1, 2, 3, 4, 5 |
| Multiple modes (bimodal/multimodal) | Two or more distinct "clusters" or common values exist | Shoe sizes 8 and 10 both most common |
Reading skew: when mean, median, and mode diverge noticeably, it's a strong signal your data is skewed rather than symmetric — worth checking before applying statistics (like standard deviation) that assume roughly normal data.
Manual verification: re-sort your dataset by hand and count to the (n+1)/2 position (or average the two middle positions for even n) to confirm the median. Tally each value's occurrences to confirm the mode, and subtract the smallest from the largest listed value to confirm the range.
Where the "typical" or "most common" value matters more than the average
Check homework on median, mode, and range calculations step by step.
Quickly verify median and mode answers for entrance and certification tests.
Use median for robust imputation of missing values and mode for encoding categorical features.
Report median home prices or median household income, which resist distortion from a few extreme values.
Find the mode to identify the most commonly purchased size, color, or product.
Use range as a fast, rough spread check on a batch of measurements.
Use mode to find the most common response in categorical survey data.
Compare median test scores against the mean to detect skew from a few outlier scores.
Find the median performance time, resistant to one unusually fast or slow outlier result.
Report median patient wait time or recovery time, which resists distortion from rare extreme cases.
Find your median monthly expense, less skewed by one unusually large purchase than the average.
Use mode to identify the most likely outcome in a set of simulated or observed results.
Get a fast summary of central tendency and spread before deeper statistical modeling.
What this median and mode calculator does well, and where care is still needed
The three measures of central tendency, side by side
| Aspect | Mean | Median | Mode |
|---|---|---|---|
| Definition | Sum ÷ count | Middle value of sorted data | Most frequent value(s) |
| Outlier sensitivity | High — pulled toward extreme values | Low — depends only on rank | None — depends only on frequency |
| Works on categorical data? | No | No | Yes |
| Always exists & unique? | Yes | Yes | No — may not exist or may be multimodal |
| Best for | Symmetric numeric data, further statistics (SD, variance) | Skewed data (income, prices) | Categorical or repeating data (sizes, ratings) |
Summary: This median and mode calculator gives you an instant, free way to find the median, mode, minimum, maximum, and range of any dataset, with the full sorted list to verify every result. Pair it with related tools like the Average Calculator and Standard Deviation Calculator for a complete statistical summary.
Common questions about median, mode and range
Trusted educational references to go deeper on the statistics behind this calculator
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